A precise linear power amplifier can be used in various electronic applications, such as, for example, controlling an electric motor. As there is generally no ripple at the output of such a linear amplifier, it also possesses a very good signal-to-noise ratio (SNR). Current ripple is considered to be a drawback in an electric circuit, especially if it is used to control an electric motor for very precise positioning, since the vibrations generated by these ripples lead to a loss of positioning precision. To do so, a control voltage, which may be direct current, is applied to the input of the linear amplifier in order to supply a fixed current through a load at the output of the linear amplifier. This current is controlled by feedback, using the current measured at the load. The amplifier's output load may consist of the electric motor to be operated. Thus, the force generated in the motor is dependent on the current through the load, which may be partly resistive and inductive. Additionally, the load may have a voltage induced by the motor itself, which is proportional to the speed of movement.
A conventional linear power amplifier, which is connected to a DC power source, generally dissipates a considerable amount of thermal power. This results from the fact that the output stage must support the entire voltage drop between the voltage at one of the terminals of the supply voltage source and the voltage at the load through which the strong current passes. Significantly, one of the power transistors of the output stage is crossed by this strong current. This voltage difference, multiplied by the current through the load, provides the total power dissipation of the linear amplifier.
For example, for a DC supply voltage on the order of 48 V and a load voltage of around 20 V, with a current of 20 A, the power dissipated by one of the power transistors of the output stage can be on the order of 560 W. As a result, the output stage of such a linear power amplifier gets extremely hot. Therefore, it is necessary that an electronic circuit that includes such a linear power amplifier be designed to dissipate the least amount of thermal energy, since it may be employed in a device used in places where the temperature must be carefully controlled. In the case where a linear power amplifier equips a device placed, for example, in a clean room for integrated circuit manufacturing, it is necessary to reduce any thermal dissipation so that the clean room does not have to be supplied with a powerful air-conditioning system.
To resolve the problem of significant thermal dissipation in an electronic circuit, the conventional linear power amplifier may beneficially be combined in parallel with a switched-mode amplifier or amplification unit. In this case, the major part of the current across the load passes through the switched-mode amplifier instead of the output stage of the linear amplifier. In principal, once stabilized, the mean output current of the linear amplifier is close to 0 A. Nevertheless, some residual heat dissipation is found in the linear power amplifier, since the instantaneous value of the current is not zero. By using an electronic circuit with a linear amplifier assisted by a switched-mode amplifier, thermal dissipation is greatly reduced.
In this context, according to the article written by Hans Ertl, Johann W. Kolar, and Franz C. Zach, “Basic Consideration and Topologies of Switched-Mode Assisted Linear Power Amplifiers,” published in IEEE Transactions on Industrial Electronics, Col. 44, No. 1, February 1997, an electronic circuit with a linear amplifier assisted by a switched-mode amplification unit is shown in FIG. 1a. 
The electronic circuit 1 of FIG. 1a, therefore, principally includes a linear power amplifier 2 and a switched-mode amplification unit 3. Linear power amplifier 2 includes an operational amplifier 4 whose non-inverting input terminal receives a reference voltage IN for determining the voltage applied to the load Z at the output. A resistive divider, which includes two resistors R1 and R2, is connected to load Z at the output of linear amplifier 2 and to a reference voltage, which is preferably 0 V, such as a ground terminal. The connecting node of the two resistors R1 and R2 is connected to the inverting input terminal of operational amplifier 4 so that the voltage applied to load Z is dependent on the reference voltage IN. Resistors R1 and R2 can have the same resistance, which is, notably, much greater than the resistance of load Z.
Linear power amplifier 2 further includes two MOSFET type power transistors 7 and 8 connected in series between two terminals V+ and V− of a DC voltage source, which is not shown. The high potential, V+, of the supply voltage source can be, for example, on the order of 24 V, while the low potential, V−, of said supply voltage source can be, for example, on the order of −24 V. The drain of first n-type MOSFET transistor 7 is connected to the high potential terminal V+ of the supply voltage source, and the source is connected to the source of the second p-type MOSFET transistor 8 and to load Z. The drain of second p-type MOSFET transistor 8 is connected to the low potential terminal V− of the supply voltage source. The gates of first and second power transistors 7 and 8 are connected, respectively, by a first voltage source 5 and a second voltage source 6 to the output of operational amplifier 4. Each voltage source is used primarily to polarize to a suitable level the gate of the corresponding power transistor, whose barrier voltage can be greater than 5 V. In a conventional manner, each voltage source 5 and 6 can be used to more rapidly initiate conduction of corresponding power transistors 7 and 8 based on a voltage fluctuation at the output of operational amplifier 4.
Each MOSFET power transistor 7 and 8 in the output stage is brought to the conductive state based on current I1 supplied at the output of linear amplifier 2 to load Z. In the case where the value of current I1 is positive, first power transistor 7 is brought to the conductive state, whereas in the case where this current I1 has a negative value, it is the second power transistor 8 that is brought to the conductive state.
The conventional system described above also includes the use of a switched-mode amplification unit 3, which supplies a current I2 to load Z with a certain delay with respect to the activation of linear amplifier 2, as explained below. Addition of the two currents, I1 and I2, corresponds to the current I across said load Z.
Switched-mode amplification unit 3 of electronic circuit 1 of FIG. 1a includes a hysteresis controller 11, which receives a current value I1 measured by a current sensor 10 at the output of linear power amplifier 2. This hysteresis controller 11 provides a control signal to a buffer 12, which is connected to the gate of a first n-type MOSFET power transistor 13 and to an inverter 14, which is connected to the gate of a second n-type MOSFET power transistor 15. The drain of first n-type MOSFET power transistor 13 is connected to the high-potential terminal V+ of the supply voltage source, while the source of the second n-type MOSFET power transistor 15 is connected to the low-potential terminal V− of the supply voltage source. The source of first transistor 13 and the drain of second transistor 15 are connected to an inductor L, which is itself connected to load Z in order to supply current I2.
The voltage level of the control signal at the output of the hysteresis controller is used to bring into the conductive state, alternately and cyclically, either first power transistor 13 or second power transistor 15. Once current I1, measured by sensor 10, reaches a first hysteresis controller threshold, conduction of power transistors 13 and 15 is switched. Conduction switching of the power transistors inversely modifies the increase or decrease of current I2 supplied by the switched-mode amplification unit through inductor L. Depending on the increase or decrease of current I2 following the switching of power transistors 13 and 15, current I1 decreases or increases up to a second threshold of hysteresis controller 11. The addition of currents I1 and I2, in principle, does not modify the defined current I across load Z, since the voltage applied to the load's terminals is controlled by linear amplifier 2. Once current I1, measured by sensor 10, reaches the second threshold of hysteresis controller 11, the conduction of power transistors 13 and 15 is again switched. Power transistors 13 and 15 are again switched over time and cyclically based on switching period T. This creates a ripple in currents I1 and I2. On the other hand, the mean of current I1 is near 0 A once stabilized.
An electronic circuit with a switched-mode assisted linear amplifier unit whose structure is appreciably identical to that of the electronic circuit of FIG. 1a is described in an article written by Geoffrey R. Walker, entitled “A Class-B Switch-Mode Assisted Linear Amplifier,” published in IEEE Transactions on Power Electronics, Col. 18, No. 6, November 2003. The main difference of this electronic circuit is that current I1 is measured by a first sensor at the drain of the first power transistor of the output stage of the linear amplifier and by a second sensor at the drain of the second power transistor. A first hysteresis controller of the switched-mode unit receives the value of current I1 from the first sensor, whereas a second hysteresis controller receives the value of current I1 from the second sensor. The switching principle of the power transistors of the switched-mode unit, however, is identical to what has been described with reference to FIG. 1a. Consequently, this electronic circuit has the same drawbacks as the electronic circuit of FIG. 1A.
To control the motor, the current circulating in the load needs to be controlled. To do this, a proportional-integral (PI) type controller is typically used, which is conventional in current practice. For example, reference is made to the article by R. Pastorino, M. A. Naya, J. A. Pérez, and J. Cuadrado entitled “X-by-Wire Vehicle Prototype: A Steer-by-Wire System with Geared PM Coreless Motors,” published for the 7th Euromech Solid Mechanics conference held in Lisbon, Portugal, in September 2009. FIG. 3 of this article shows an example of current feedback by a linear amplifier and PI controller, whose operation is detailed in section 3.1.1.
FIG. 1b illustrates an improved configuration of electronic circuit 1 presented in FIG. 1a, in which the current is load compensated. Linear amplifier unit 20 includes a first current feedback loop. Notably, linear amplifier unit 20 includes a first subtractor element 23 of first current feedback loop. In this subtractor element 23, the current Im1, which is measured across load Z by first sensor 25 in series with the load, is subtracted from the reference current Iref, which is the current setpoint. The result of the subtraction is supplied to a first controller 24, which is preferably a conventional PI controller. This controller 24 supplies a control voltage to linear amplifier 2, which outputs a first current I1 that will cross load Z. The value of this current I1 is modified by linear amplifier unit 20 based on the voltage level detected at the load and, primarily, on measurement of the current I across the load. On the other hand, switched-mode amplification unit 3 includes the same elements as those described with reference to FIG. 1a, with current I1 measured by second sensor 10 being supplied to the input of the unit 3.
FIG. 1c shows another configuration of electronic circuit 1 shown in FIG. 1b. The main difference of electronic circuit 1 of this FIG. 1c is that the hysteresis controller is replaced by a second PI controller 31. In effect, the hysteresis controller includes certain drawbacks that will be detailed below, and it is desirable that it be replaced by a PI controller placed in series with a pulse-width modulator (PWM) 33 that controls the gate of power transistors 13 and 15. The operation of such a modulator 33 is known and is, for example, represented in FIG. 3 of U.S. Pat. No. 7,385,363. Therefore, no detailed information is provided regarding its internal operation. The modulator of U.S. Pat. No. 7,385,363 is used to switch power transistors 13 and 15 at constant frequency, which is not the case for the hysteresis controller of FIGS. 1a and 1b. 
FIG. 2a graphically represents the variation in currents I1 and I2 over time based on a current setpoint Iref supplied initially to linear amplifier unit 20 of electronic circuit 1 of FIG. 1b. This electronic circuit includes hysteresis controller 11 in switched-mode amplification unit 3. Based on the setpoint, a current, Iref, will cross the load as it leaves the linear amplifier unit and the switched-mode amplification unit. In this example, current Iref is defined sinusoidally at a frequency of 1 kHz and an amplitude of 1 A.
In the graph at the top of FIG. 2a, it is seen that the current in load I very closely follows setpoint Iref. The observed phase difference, as well as the slight decrease in amplitude, are associated with the bandwidth of the current feedback from the linear amplifier unit. However, this total current is the sum of current I1 supplied by the linear amplifier unit and current I2 from the switched-mode amplification unit. The shape of these currents is shown in the graph at the bottom of FIG. 2a. 
Once current I1 falls below 0 A to reach a first threshold of the hysteresis controller, the conduction of the power transistors is switched in the switched-mode unit. After switching, current I2 will decrease, whereas current I1 will increase to a second threshold of the hysteresis controller, whereby the power transistors of the switched-mode unit are switched once again. The difference between the first threshold and the second threshold of the controller represents a current difference ΔI, which can be adjusted. Switching of the power transistors of the switched-mode unit is repeated cyclically based on a switching period T.
Because current I1 at the output of the linear amplifier is not zero, some residual dissipation remains in the linear amplifier, which is a drawback. The smaller the current difference, ΔI, of the hysteresis controller, the greater the switching frequency of the power transistors in the switched-mode unit, which has a tendency to increase the switching losses of the electronic circuit. However, by increasing the current difference, ΔI, of the hysteresis controller, switching occurs less frequently while the switching period T increases, but more heat is dissipated by the linear amplifier. Additionally, depending on the value of the current setpoint supplied at the input of the linear amplifier unit, setpoint variations, and voltage variations induced in the motor, the switching period T will vary, which is a drawback. This frequency variation is clearly visible on the time-based curve and can, in particular, lead to problems of electromagnetic compatibility in the circuit.
To produce a satisfactory electronic circuit, a compromise must be sought between hysteresis and heat dissipation, as well as a dynamic compromise relative to the bandwidth of the switched-mode amplification unit and heat dissipation. With an electronic circuit as shown in FIG. 1a or 1b, normally, the signal-to-noise ratio can never be greater than 80 dB, which is a disadvantage. In this example, the root-mean-square (RMS) value of residual current I1 is 70.3 mA. This current can be used to estimate the thermal dissipation in the linear amplifier.
FIG. 2b graphically represents the current variation obtained with the electronic circuit of FIG. 1c, in which the hysteresis controller is replaced by PI controller 31 placed in series with PWM modulator 33. In the graph at the top of FIG. 2b, it is seen that the shape of the current in the load, I, is identical to that of FIG. 2a. In effect, the total current I depends only on the feedback occurring in linear amplifier unit 20.
In the graph at the bottom of FIG. 2b, it is seen that the switching period T is constant due to the use of PWM modulator 33, which is advantageous. On the other hand, residual current I1 has increased in comparison to that of FIG. 2a. In effect, its RMS value is now 138.6 mA. This is due to the phase delay between Iref and I1 resulting from the imperfection of the feedback occurring in linear amplifier unit 20. A second phase delay is introduced by PI controller 31. The residual current, therefore, includes a sinusoidal component that is clearly visible in FIG. 2b, in addition to the ripples associated with switching of the switched-mode unit.